Download or read book Existence Theorems for Ordinary Differential Equations written by Francis J. Murray and published by Courier Corporation. This book was released on 2013-11-07 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition.
Download or read book Some Fundamental Existence Theorems for Differential Systems written by Penelope Carter Crockett and published by . This book was released on 1963 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Existence Theorems in Partial Differential Equations written by Dorothy L. Bernstein and published by Princeton University Press. This book was released on 1951-01-20 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic treatment of existence theorems in partial differential equations from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Download or read book Fundamental Existence Theorems written by Gilbert Ames Bliss and published by . This book was released on 1913 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basic Theory of Ordinary Differential Equations written by Po-Fang Hsieh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.
Download or read book Existence Theory for Nonlinear Ordinary Differential Equations written by Donal O'Regan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
Download or read book Existence Theorems for Certain Classes of Two point Boundary Problems by Variational Methods written by Richard James Driscoll and published by . This book was released on 1959 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ordinary Differential Equations written by Wolfgang Walter and published by Springer Science & Business Media. This book was released on 2013-03-11 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.
Download or read book Two Point Boundary Value Problems Lower and Upper Solutions written by C. De Coster and published by Elsevier. This book was released on 2006-03-21 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.· Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
Download or read book The Fundamental Existence Theorem for Differential Equations by Topological Methods written by Dixie Russell Russell and published by . This book was released on 1966 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Differential Equations written by Andrew Russell Forsyth and published by . This book was released on 1900 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Differential Equations written by Andrew Russell Forsyth and published by CUP Archive. This book was released on 1959 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Existence Theorems and Certain Applications for Ordinary Differential Equations written by James Graham Wall and published by . This book was released on 1933 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Existence Theorems from Classical Analysis written by Margaret Mary Schmieg and published by . This book was released on 1956 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Existence Theorems for Ordinary Differential Equations written by Cullen Squaere Hodge and published by . This book was released on 1950 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The general solution of the first order linear differential equation, F(x, y, y0́9) = 0 (1.1.1), is an equation connecting x, y and an arbitrary constant. We assume P to be a single-valued function throughout some domain and that y is a differentiable function of x. Under certain conditions (Goursat 5, Chap. 2) we may write 1.1.1 in the form, y0́9 = f(x, y) (1.1.2), where f(x, y) is continuous (simultaneously) in x and y in a domain S." --
Download or read book Ordinary Differential Equations And Boundary Value Problems Volume I Advanced Ordinary Differential Equations written by John R Graef and published by World Scientific. This book was released on 2018-02-13 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book.The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well.Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems.Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs.
Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Society. This book was released on 2024-01-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
